Unfortunately, this data doesn't appear to be freely available. It can be purchased from the New Mexico Secretary of State's Office here, in accordance with Section 126.96.36.199 of the New Mexico Administrative Code:
188.8.131.52 VOTER RECORDS REQUESTS:
A. All requesters of voter file data or public service requests shall
complete the affidavit of authorization prescribed by the secretary of
B. The secretary of state shall develop a uniform fee schedule for
data recording media, voter data, voter lists, special voter lists,
precinct lists, printed labels, and early and absentee daily voting
reports. County clerks may require a deposit for any data requested.
Source - LII
The only other journalistic source that seems to be publishing this information is the Albequerque Journal (May 6th). The author of that article has released updated data from May 10th on his Twitter account.